# Circle Formula

Circle is a particular shape and defined as the set of points in a plane placed at equal distance from a single point called the center of the circle. We use the circle formula to calculate the area, diameter, and circumference of a circle. The length between any point on the circle and its center is known as its radius.Any line that passes through the center of the circle and connects two points of the circle is known as the diameter of the circle. Radius is half the length of a diameter of the circle. Area of the circle describes the amount of space covered by the circle and the length of the boundary of the circle is known as its circumference.

Where,

• r denotes the radius of the circle.
• d indicates the diameter of the circle.
• c indicates circumference of the circle.

## Formulas Related to Circles

The Circle Formulas are expressed as,

 Diameter of a Circle D = 2 × r Circumference of a Circle C = 2 × π × r Area of a Circle A = π × r2

### Example Question Using the Circle Formulas

Example 1

A circle has a radius 8 cm. Calculate its diameter, area and circumference.

Solution

Given parameters are,

Diameter of a circle is given by

2r

= 2 × 8 cm

= 16 cm

Area of a circle is given by

π r2

= π × 64

= 201.088 cm2

Circumference of a circle is given by

2 π r

= 2 × π × 8

= 50.272 cm

Example 2

Find the diameter, area and circumference of a circle of radius 15 cm.

Solution

Given parameters are

Radius of a circle, r = 15 cm

Diameter of a circle is given by

2r

= 2 × 15

= 30 cm

Area of a circle is given by

π r2

= π ×152

= π × 225

= 706.95 cm2

Circumference of a circle

= 2 π r

= 2 × π × 15

= 94.26 cm

#### Practise This Question

A string of linear mass density 0.5 g cm1 and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end. The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of 20 cms1. The pulse is symmetric about its maximum which is located at a distance of 20 cm from the end joined to the ring. Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape.